Using empirical Bayes predictors from generalized linear mixed models to test and visualize associations among...

Area of Science:

• Biostatistics
• Medical Statistics
• Longitudinal Data Analysis

Background:

• Medical research frequently involves repeated measurements on subjects.
• Analyzing associations among non-normal, repeatedly measured outcomes requires advanced statistical methods.
• Multivariate generalized linear mixed models (MGLMMs) can model latent relationships among such outcomes.

Purpose of the Study:

• To evaluate the utility of second-stage association analyses using empirical Bayes predictors from MGLMMs.
• To compare MGLMM-based analyses with analyses using empirical Bayes predictors from separate mixed models.
• To assess the approximation and visual representation of latent associations.

Main Methods:

• Utilized multivariate generalized linear mixed models (MGLMMs) to model latent associations.
• Employed empirical Bayes predictors derived from MGLMMs and separate mixed models.
• Conducted simulation studies and analyzed medical examples.
• Compared p-values from normality assumptions with permutation analyses.

Main Results:

• Second-stage analyses of MGLMM empirical Bayes predictors provide a good approximation of latent associations.
• P-values derived from assuming normality of empirical Bayes predictors closely match permutation-based p-values.
• Analyzing interrelated outcomes with separate models leads to different parameter estimates and potential inference errors compared to MGLMMs.

Conclusions:

• Scatterplots of empirical Bayes predictors from MGLMMs are preferable for visualizing latent associations when computable.
• Separate modeling of outcomes can introduce bias, especially with strong inter-outcome associations.
• MGLMMs offer a more accurate approach to analyzing complex associations in longitudinal medical data.